The Nazis did not plan to capture Leningrad at this point. Rather, their plan was to drive many people into Leningrad and then starve them there, as laid out in the Hunger Plan. The Hunger Plan called for the mass murder of 20 million people via starvation.
The wikipedia on the siege of Leningrad has also some details:
Army Group North under Feldmarschall Wilhelm Ritter von Leeb advanced to Leningrad, its primary objective. Von Leeb's plan called for capturing the city on the move, but due to Hitler's recall of 4th Panzer Group (persuaded by his Chief of General Staff, Franz Halder, to transfer this south to participate in Fedor von Bock's push for Moscow), von Leeb had to lay the city under siege indefinitely after reaching the shores of Lake Ladoga, while trying to complete the encirclement and reaching the Finnish Army under Marshal Carl Gustaf Emil Mannerheim waiting at the Svir River, east of Leningrad.
Finnish military forces were located north of Leningrad, while German forces occupied territories to the south. Both German and Finnish forces had the goal of encircling Leningrad and maintaining the blockade perimeter, thus cutting off all communication with the city and preventing the defenders from receiving any supplies. The Germans planned on lack of food being their chief weapon against the citizens; German scientists had calculated that the city would reach starvation after only a few weeks.
I think it likely that local Wehrmacht commanders wanted to take the city at one point or other, but ultimatley the grand strategy called for encircling and siege beforehand.
Despite attempts to feed and evacuate the city via the frozen lake, a million civilians lost their lives. The conditions in the city were desperate, to put it very mildly.
I think this question comes from looking at the siege of Leningrad as a purely military set piece, and sees just a baffling military decision to not take the city. I think you need to look at the political and economic goals of the Nazis, and at the immense suffering of the people in Leningrad.
Further Details on the Hunger Plan can be found in Götz Aly's "Vordenker der Vernichtung"
and Felix Wemheuer's "Der Große Hunger: Hungersnöte unter Stalin und Mao"
Both should be available in english.
If you read German, here's a lengthy excerpt about the Hunger Plan and the siege of Leningrad from the latter.